The fragmentation equation with size diffusion: Well posedness and long-term behaviour

2021 ◽  
pp. 1-34 ◽  
Author(s):  
PH. LAURENÇOT ◽  
CH. WALKER
Keyword(s):  
Linear Operator ◽  
Stationary Solution ◽  
Analytic Semigroup ◽  
Well Posedness ◽  
Exponential Rate ◽  
Initial Value ◽  
One Dimensional ◽  
Fragmentation Rate ◽  
Fragmentation Equation

The dynamics of the fragmentation equation with size diffusion is investigated when the size ranges in $(0,\infty)$ . The associated linear operator involves three terms and can be seen as a nonlocal perturbation of a Schrödinger operator. A Miyadera perturbation argument is used to prove that it is the generator of a positive, analytic semigroup on a weighted $L_1$ -space. Moreover, if the overall fragmentation rate does not vanish at infinity, then there is a unique stationary solution with given mass. Assuming further that the overall fragmentation rate diverges to infinity for large sizes implies the immediate compactness of the semigroup and that it eventually stabilizes at an exponential rate to a one-dimensional projection carrying the information of the mass of the initial value.

A proof of the well posedness of discretized wave equation with an absorbing boundary condition

2014 ◽  
Vol 22 (4) ◽  
Author(s):  
I. Alonso-Mallo ◽  
A.M. Portillo
Keyword(s):  
Wave Equation ◽  
Numerical Experiments ◽  
Necessary Conditions ◽  
Absorbing Boundary Conditions ◽  
Well Posedness ◽  
Initial Value ◽  
Absorbing Boundary ◽  
One Dimensional ◽  
The One ◽  
Fifth Order

Abstract- Local absorbing boundary conditions with fifth order of absorption to approximate the solution of an initial value problem, for the spatially discretized wave equation, are considered. For the one dimensional case, it is proved necessary conditions for well posedness. Numerical experiments confirming well posedness and showing good results of absorption are included.

LINEAR TRANSPORT OF PARTICLES ON NETWORKS

1996 ◽  
Vol 06 (02) ◽  
pp. 279-294 ◽  
Author(s):  
LUIGI BARLETTI
Keyword(s):  
Boundary Conditions ◽  
Initial Value Problem ◽  
Connected Graph ◽  
Well Posedness ◽  
Linear Boundary ◽  
Initial Value ◽  
One Dimensional ◽  
Linear Transport ◽  
Streaming Transport

We introduce a model of transport of particles in a network, which is represented by a connected graph with m vertices and n edges. Each edge represents a one-dimensional conductor of particles, whose behavior is described by means of a linear Boltzmann-like equation. In graph vertices, a system of linear boundary conditions is given which takes into account the exchanges of particles between the edges. The well-posedness of the initial value problem is studied into an abstract L1-like setting and the structure of the solution is given for simplest case of pure streaming transport.

scholarly journals Indoor radon concentration and a diffusion model in dwellings situated in a subalkaline granitoid area, Southern Brazil

2021 ◽  
Vol 80 (17) ◽  
Author(s):  
G. Romero-Mujalli ◽  
A. Roisenberg ◽  
A. Cordova-Gonzalez ◽  
P. H. P. Stefano
Keyword(s):  
Diffusion Model ◽  
Indoor Radon ◽  
Southern Brazil ◽  
High Concentration ◽  
Indoor Radon Concentration ◽  
One Dimensional ◽  
Environmental Limits ◽  
Radon Measurements ◽  
Cr 39 Detectors

AbstractRadon (Rn), a radioactive element, has especial interest in medical geology because long-term exposure to high concentration is related to lung cancer. In this study, outdoor and indoor radon measurements were conducted in dwellings of the Piquiri Syenite Massif, located in southern Brazil, given the relative high Rn content in soils of this region. Measurements were done using CR-39 detectors and placing them inside and outside dwellings. Moreover, a one-dimensional diffusion model was performed in order to quantify the natural transport of Rn to the air in confined and aerated environments. Results indicate that the region presents relatively low air Rn concentrations, within the environmental limits; however, the health risk might increase in confined and ill-ventilated environments because of transfer from soil and exhalation from ornamental rock-material often found inside dwellings. The main north facies of the syenite, where most of the rock extractions are located, was found to have the highest air Rn concentration because of the higher soil Rn concentration, compared to other facies of the syenite.

scholarly journals ENERGY CRITICAL NLS IN TWO SPACE DIMENSIONS

2009 ◽  
Vol 06 (03) ◽  
pp. 549-575 ◽  
Author(s):  
J. COLLIANDER ◽  
S. IBRAHIM ◽  
M. MAJDOUB ◽  
N. MASMOUDI
Keyword(s):  
Schrödinger Equation ◽  
Initial Value Problem ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Energy Space ◽  
Well Posedness ◽  
Initial Value ◽  
Exponential Nonlinearity ◽  
Supercritical Case ◽  
Two Space Dimensions

We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exponential nonlinearity [Formula: see text] We identify subcritical, critical, and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case.

Suspending Damage: A Letter to Communities

2009 ◽  
Vol 79 (3) ◽  
pp. 409-428 ◽  
Author(s):  
Eve Tuck
Keyword(s):  
Theory Of Change ◽  
Open Letter ◽  
One Dimensional ◽  
Marginalized Communities ◽  
Long Term Impact

In this open letter, Eve Tuck calls on communities, researchers, and educators to reconsider the long-term impact of "damage-centered" research—research that intends to document peoples' pain and brokenness to hold those in power accountable for their oppression. This kind of research operates with a flawed theory of change: it is often used to leverage reparations or resources for marginalized communities yet simultaneously reinforces and reinscribes a one-dimensional notion of these people as depleted,ruined, and hopeless. Tuck urges communities to institute a moratorium on damage-centered research to reformulate the ways research is framed and conducted and to reimagine how findings might be used by, for, and with communities.

Sign in / Sign up

Export Citation Format

Share Document